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Question

The value of $$\displaystyle\ \frac{\sqrt{7}+2}{\sqrt{7}-2} + \frac{\sqrt{7}-2}{\sqrt{7}+2}$$ is $$\displaystyle\ \frac{8\sqrt{7}}{m}$$, then the value of$$m$$ is ?


Solution

$$\dfrac { \sqrt { 7 } +2 }{ \sqrt { 7 } -2 } +\dfrac { \sqrt { 7 } -2 }{ \sqrt { 7 } +2 } =\dfrac { (\sqrt { 7 } +2)(\sqrt { 7 } +2)+(\sqrt { 7 } -2)(\sqrt { 7 } -2) }{ (\sqrt { 7 } +2)(\sqrt { 7 } -2) } \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\dfrac { 8\sqrt { 7 }  }{ 3 } $$ 

on comparing  $$\dfrac { 8\sqrt { 7 }  }{ m }$$ by our answer we get $$m=3$$

Mathematics

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